WASHINGTON — President Donald Trump on Sunday abandoned a strategy of showing deference to the special counsel examining Russia’s interference in the 2016 presidential election, lashing out at what he characterized as a partisan investigation and alarming Republicans who feared he might seek to shut it down.

Trump has long suggested that allegations that he or his campaign conspired with Russia to influence the election were a “hoax” and part of a “witch hunt,” but until this weekend he had largely heeded the advice of lawyers who counseled him not to directly attack Robert Mueller, the special counsel, for fear of antagonizing prosecutors.

“Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans?” Trump wrote on Twitter. “Another Dem recently added...does anyone think this is fair? And yet, there is NO COLLUSION!”

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The attack on Mueller, a longtime Republican and former FBI director appointed by a Republican president, George W. Bush, drew immediate rebukes from some members of the party who expressed concern that it might presage an effort to fire the special counsel. Such a move, they warned, would give the appearance of a corrupt attempt to short-circuit the investigation and set off a bipartisan backlash.

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“If he tried to do that, that would be the beginning of the end of his presidency, because we’re a rule-of-law nation,” Sen. Lindsey Graham, R-S.C., an ally of the president, said on “State of the Union” on CNN. “When it comes to Mr. Mueller, he is following the evidence where it takes him, and I think it’s very important he be allowed to do his job without interference, and there are many Republicans who share my view.”

Among them was Sen. Jeff Flake of Arizona, a sharp critic of Trump who appeared on the same program. “People see that as a massive red line that can’t be crossed,” he said. He urged Trump’s advisers to prevail on him not to fire Mueller. “We have confidence in Mueller.”

Rep. Trey Gowdy, R-S.C., said if the president was innocent, he should “act like it” and leave Mueller alone, warning of dire repercussions if the president tried to fire the special counsel.

“I would just counsel the president — it’s going to be a very, very long, bad 2018, and it’s going to be distracting from other things that he wants to do and he was elected do,” Gowdy said on “Fox News Sunday.” “Let it play out its course. If you’ve done nothing wrong, you should want the investigation to be as fulsome and thorough as possible.”

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The House speaker, Paul D. Ryan, R-Wis., issued a statement likewise warning Trump to back off. “As the speaker has always said, Mr. Mueller and his team should be able to do their job,” said AshLee Strong, a spokeswoman. His counterpart, Sen. Mitch McConnell of Kentucky, had no comment, as did a number of other top Senate Republicans.

Late in the day, the White House tried to douse the furor. “In response to media speculation and related questions being posed to the administration, the White House yet again confirms that the president is not considering or discussing the firing of the special counsel, Robert Mueller,” Ty Cobb, a White House lawyer, said in a statement.

The president’s tweet followed a statement by Trump’s personal lawyer, John Dowd, on Saturday calling on the Justice Department to end the special counsel investigation. Trump followed up that evening with a tweet arguing that “the Mueller probe should never have been started in that there was no collusion and there was no crime.”

The two weekend tweets were the first time Trump has used Mueller’s name on Twitter, not counting a message he once retweeted, and reflected what advisers called a growing impatience fueled by anger that the investigation was now looking at his business activities.

The New York Times reported last week that Mueller has subpoenaed records from the Trump Organization. Trump’s lawyers met with Mueller’s team last week and received more details about how the special counsel is approaching the investigation, including the scope of his interest in the Trump Organization.

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For months, Trump had been reassured by his lawyers that the investigation would wrap up soon — by Thanksgiving, then Christmas, then New Year’s. But with the expansion into Trump’s business, it seems increasingly clear that Mueller is not ready to conclude his inquiry.

A top adviser to Trump said on Sunday that the White House had grown weary of the inquiry. “We have cooperated in every single way, every single paper they’ve asked for, every single interview,” Marc Short, the president’s legislative director, said on “Face the Nation” on CBS. “There’s a growing frustration that after a year and millions and millions of dollars spent on this, there remains no evidence of collusion with Russia.”

A president cannot directly fire a special counsel but can order his attorney general to do so. Even then, a cause has to be cited, like conflict of interest. Since Attorney General Jeff Sessions, a former campaign adviser, has recused himself from the Russia investigation — to Trump’s continuing irritation — the task would fall to the deputy attorney general, Rod J. Rosenstein.

But Rosenstein said as recently as last week that he sees no justification for firing Mueller, meaning that he would either have to change his mind or be removed himself. The third-ranking official at the Justice Department, Rachel Brand, knowing this issue could reach her, decided last month to step down. The next official in line would be the solicitor general, Noel Francisco, a former White House and Justice Department lawyer under Bush.

Trump sought to have Mueller fired last June but backed down after his White House counsel, Donald F. McGahn II, threatened to quit. The president told The Times a month later that Mueller would be crossing a red line if he looked into his family’s finances beyond any relationship with Russia.

The White House made no assertion last week that the subpoena to the Trump Organization crossed that red line, but Trump evidently has grown tired of the strategy of being respectful to the special counsel. His focus on Democrats working for Mueller could be aimed at demonstrating conflict of interest that would merit dismissal.

When Mueller assembled his team, he surrounded himself with trusted former colleagues and experts on specific crimes like money laundering. As the team filled out, Republican allies of Trump noted that some members had previously contributed to Democratic candidates.

In particular, Republicans pointed to Andrew Weissmann, who served as FBI general counsel under Mueller. Weissmann is a career prosecutor but, while in private law practice, donated thousands of dollars toward President Barack Obama’s election effort.

In his Sunday morning Twitter blasts, Trump also renewed his attacks on James B. Comey, the former FBI director, and Andrew G. McCabe, his former deputy, both of whom, like Mueller, are longtime Republicans. Trump fired Comey last May, at first attributing the decision to the FBI director’s handling of the investigation into Hillary Clinton’s private email server but later telling an interviewer that he had the Russia investigation in mind when he made the decision.

Sessions, under intense public pressure from Trump, fired McCabe on Friday after an inspector general found that he had not been forthcoming about authorizing FBI officials to provide information about the Clinton inquiry in 2016 to a reporter.

“Wow, watch Comey lie under oath to Senator G when asked ‘have you ever been an anonymous source...or known someone else to be an anonymous source...?’” Trump wrote. “He said strongly ‘never, no.’ He lied as shown clearly on @foxandfriends.”

Trump went on to dismiss reports that McCabe kept detailed memos of his time as deputy FBI director, just as Comey did. McCabe left those memos with the FBI, which means Mueller’s team has access to them.

“Spent very little time with Andrew McCabe, but he never took notes when he was with me,” Trump wrote. “I don’t believe he made memos except to help his own agenda, probably at a later date. Same with lying James Comey. Can we call them Fake Memos?”

Michael R. Bromwich, McCabe’s lawyer, fired back by accusing the president of corrupting the law enforcement system. “We will not be responding to each childish, defamatory, disgusting & false tweet by the President,” he wrote on Twitter. “The whole truth will come out in due course. But the tweets confirm that he has corrupted the entire process that led to Mr. McCabe’s termination and has rendered it illegitimate.”

In suggesting that Comey lied under oath to Congress, Trump appeared to refer to a comment by McCabe that the former director had authorized the media interaction at the heart of the complaint against him. The president’s Republican allies picked up the point on Sunday and pressed for appointment of a prosecutor to look at the origin of the Russia investigation.

“So we know that McCabe has lied” because the inspector general concluded he had not been fully candid, Rep. Kevin McCarthy of California, the House majority leader, said on Fox News. “Now he’s saying about Comey — Comey may have lied as well. So I don’t think this is the end of it. But that’s why we need a second special counsel.”

Other Republicans, however, suggested that the Trump administration was going too far. Sen. Marco Rubio of Florida criticized the decision to fire McCabe on a Friday night shortly before his retirement took effect, jeopardizing his pension.

“I don’t like the way it happened,” Rubio said on “Meet the Press” on NBC. “He should’ve been allowed to finish through the weekend.” Speaking of the president, he added: “Obviously he doesn’t like McCabe, and he’s made that pretty clear now for over a year. We need to be very careful about taking these very important entities and smearing everybody in them with a broad stroke.”